We study two newly discovered classes of radio sources: the highly energetic, short-lived events, known as Fast Radio Bursts (FRBs), and a new category of compact radio galaxies known as Fanaroff-Riley type 0 (FR0s). Due to the unknown nature of FRBs and a previous correlation found with an FR0 in $\gamma$-rays, it is possible that these sources could also emit high energy photons in the Fermi-LAT energy range. Here we present an exhaustive time-dependent and spatial search of all up-to-date observed FRBs and FR0s, respectively. We perform a likelihood analysis of the radio sources by modeling the excess flux of gamma rays with a power law using data from Fermi-LAT and the 4FGL catalog. Sources with a pre-trial significance greater than 4$\sigma$ were further analyzed including 2 FRBs and 7 FR0s. No correlations with more than 5$\sigma$ were found after taking into account nearby sources and trial corrections. Therefore, upper limits for all sources were calculated.